Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

const int N=200100;
int a[N],b[N],f[N],g[N],n;
int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;++i)cin>>a[i],b[a[i]]=i;
	for(int i=n;i>1;--i){
		if(!f[i]){
			if(b[i]<b[i-1])f[i-1]=1,g[0]=i;
		}else{
			int u=b[i-1],v=b[i],w=b[g[f[i]-1]];
			if((w<u&&(v<w||v>u))||(u<v&&v<w))f[i-1]=f[i];
			else{
				f[i-1]=f[i]+1;
				g[f[i]]=i;
			}
		}
	}
	cout<<f[1]<<'\n';
	return 0;
}